← #10814899
Subgroups — #10814899
Order 768.
710 conjugacy classes of subgroups.
The subgroup lattice has 434 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #83897 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #78650 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C3×#1974 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #72085 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #70703 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #70694 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #70367 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #70355 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #69996 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #69783 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #69779 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #22804 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×C3×#135 | C22 | 1 | 1 | yes | characteristic |
| 14 | Dic3×#41 | C22 | 1 | 2 | yes | — |
| 15 | C2×C3×#108 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C3×#104 | C22 | 1 | 2 | yes | — |
| 17 | C3×#408 | C22 | 1 | 2 | yes | — |
| 18 | C2×C3×C4×C8 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#837 | C22 | 1 | 2 | yes | — |
| 20 | #5234 | C22 | 1 | 2 | yes | — |
| 21 | #5233 | C22 | 1 | 2 | yes | — |
| 22 | #5184 | C4 | 1 | 2 | yes | complemented |
| 23 | #5164 | C4 | 1 | 2 | yes | complemented |
| 24 | #5164 | C4 | 1 | 2 | yes | complemented |
| 25 | #5152 | C4 | 1 | 2 | yes | complemented |
| 26 | C2×#822 | C22 | 1 | 2 | yes | — |
| 27 | #5122 | C22 | 1 | 2 | yes | — |
| 28 | #5118 | C22 | 1 | 2 | yes | — |
| 29 | C2×#819 | C22 | 1 | 1 | yes | characteristic |
| 30 | #5106 | C22 | 1 | 1 | yes | characteristic |
| 31 | #5101 | C22 | 1 | 2 | yes | — |
| 32 | C2×#815 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#815 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×Dic3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 35 | C4×Dic3⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 36 | #4720 | — | 2 | 2 | no | — |
| 37 | #4720 | — | 2 | 2 | no | — |
| 38 | #4719 | — | 2 | 2 | no | — |
| 39 | #4718 | — | 2 | 2 | no | — |
| 40 | #4555 | C22 | 1 | 2 | yes | — |
| 41 | #4550 | C22 | 1 | 1 | yes | characteristic |
| 42 | #4524 | C22 | 1 | 1 | yes | characteristic |
| 43 | #4523 | C22 | 1 | 2 | yes | — |
| 44 | #2943 | — | 3 | 1 | no | — |
| 45 | #2925 | — | 3 | 2 | no | — |
| 46 | #1975 | — | 3 | 1 | no | — |
| 47 | #1974 | D3 | 1 | 1 | yes | characteristic |
| 48 | #1929 | — | 3 | 2 | no | — |
| 49 | #1929 | — | 3 | 2 | no | — |
| 50 | #1849 | — | 3 | 1 | no | — |
| 51 | #1806 | — | 3 | 2 | no | — |
| 52 | #1773 | — | 3 | 1 | no | — |
| 53 | #1772 | — | 3 | 1 | no | — |
| 54 | #1771 | — | 3 | 1 | no | — |
| 55 | C2×C3×#41 | C23 | 1 | 2 | yes | — |
| 56 | C3×#135 | — | 2 | 2 | no | — |
| 57 | C3×#135 | — | 2 | 2 | no | — |
| 58 | C2×C3×Q16 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | C2×C3×SD16 | C2×C4 | 1 | 2 | yes | — |
| 60 | C2×C3×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 61 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 62 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 63 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 65 | Q8×Dic3 | C2×C4 | 1 | 2 | yes | — |
| 66 | Q8×Dic3 | C2×C4 | 1 | 2 | yes | — |
| 67 | D4×Dic3 | — | 2 | 2 | no | — |
| 68 | D4×Dic3 | — | 2 | 2 | no | — |
| 69 | D4×Dic3 | C2×C4 | 1 | 2 | yes | — |
| 70 | D4×Dic3 | C2×C4 | 1 | 2 | yes | — |
| 71 | #926 | — | 2 | 2 | no | — |
| 72 | #926 | C23 | 1 | 2 | yes | — |
| 73 | C2×Dic3⋊C4 | — | 2 | 1 | no | — |
| 74 | C2×C4×Dic3 | — | 2 | 2 | no | — |
| 75 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 77 | C2×#208 | C23 | 1 | 2 | yes | — |
| 78 | C22×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 79 | C22×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 80 | C3×#108 | — | 2 | 2 | no | — |
| 81 | C3×#104 | — | 4 | 2 | no | — |
| 82 | C3×C22⋊C8 | — | 2 | 2 | no | — |
| 83 | C3×C22⋊C8 | — | 2 | 2 | no | — |
| 84 | C3×C4×C8 | — | 2 | 2 | no | — |
| 85 | #837 | — | 4 | 2 | no | — |
| 86 | #835 | C2×C4 | 1 | 2 | yes | — |
| 87 | #835 | C2×C4 | 1 | 2 | yes | — |
| 88 | #832 | C2×C4 | 1 | 2 | yes | — |
| 89 | #832 | C2×C4 | 1 | 2 | yes | — |
| 90 | C3⋊#95 | — | 2 | 1 | no | — |
| 91 | #830 | — | 2 | 2 | no | — |
| 92 | #830 | — | 2 | 2 | no | — |
| 93 | #822 | — | 4 | 2 | no | — |
| 94 | #819 | — | 2 | 2 | no | — |
| 95 | #818 | C2×C4 | 1 | 1 | yes | characteristic |
| 96 | #818 | C2×C4 | 1 | 1 | yes | characteristic |
| 97 | #817 | C2×C4 | 1 | 2 | yes | — |
| 98 | #815 | — | 2 | 2 | no | — |
| 99 | #815 | — | 2 | 2 | no | — |
| 100 | #815 | — | 2 | 2 | no | — |
| 101 | #815 | C2×C4 | 1 | 2 | yes | — |
| 102 | #815 | C2×C4 | 1 | 2 | yes | — |
| 103 | Dic3⋊C8 | — | 2 | 2 | no | — |
| 104 | Dic3⋊C8 | — | 2 | 2 | no | — |
| 105 | Dic3⋊C8 | D4 | 1 | 2 | yes | — |
| 106 | Dic3⋊C8 | D4 | 1 | 2 | yes | — |
| 107 | C8×Dic3 | — | 2 | 2 | no | — |
| 108 | C8×Dic3 | — | 2 | 2 | no | — |
| 109 | C2×#135 | C2×D3 | 1 | 1 | yes | characteristic |
| 110 | C4×#41 | — | 3 | 2 | no | — |
| 111 | #442 | — | 3 | 2 | no | — |
| 112 | #441 | — | 3 | 2 | no | — |
| 113 | #440 | — | 3 | 2 | no | — |
| 114 | #440 | — | 3 | 2 | no | — |
| 115 | #433 | — | 6 | 2 | no | — |
| 116 | #433 | — | 6 | 2 | no | — |
| 117 | #432 | — | 6 | 2 | no | — |
| 118 | #431 | — | 6 | 2 | no | — |
| 119 | C2×#108 | — | 3 | 1 | no | — |
| 120 | C2×#108 | — | 3 | 2 | no | — |
| 121 | C2×#108 | C2×D3 | 1 | 1 | yes | characteristic |
| 122 | #427 | — | 3 | 1 | no | — |
| 123 | #423 | — | 3 | 2 | no | — |
| 124 | C2×C4⋊C8 | — | 3 | 1 | no | — |
| 125 | C2×#104 | — | 3 | 2 | no | — |
| 126 | C2×#104 | C2×D3 | 1 | 2 | yes | — |
| 127 | #416 | — | 3 | 2 | no | — |
| 128 | #408 | — | 3 | 2 | no | — |
| 129 | #408 | C2×D3 | 1 | 2 | yes | — |
| 130 | #405 | — | 3 | 2 | no | — |
| 131 | #405 | — | 3 | 2 | no | — |
| 132 | C2×#97 | — | 3 | 1 | no | — |
| 133 | C2×#97 | — | 3 | 1 | no | — |
| 134 | C2×C4×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 135 | C4×C4⋊C4 | — | 3 | 1 | no | — |
| 136 | #339 | — | 3 | 2 | no | — |
| 137 | #339 | — | 3 | 2 | no | — |
| 138 | #336 | — | 3 | 1 | no | — |
| 139 | #336 | — | 3 | 1 | no | — |
| 140 | C3×#41 | — | 2 | 2 | no | — |
| 141 | C3×#41 | — | 2 | 2 | no | — |
| 142 | C3×#41 | — | 2 | 2 | no | — |
| 143 | C3×#41 | — | 2 | 2 | no | — |
| 144 | C2×C3×Q8 | C22×C4 | 1 | 2 | yes | — |
| 145 | C2×C3×D4 | — | 2 | 2 | no | — |
| 146 | C2×C3×D4 | C22×C4 | 1 | 2 | yes | — |
| 147 | C22×C3×C4 | — | 2 | 1 | no | — |
| 148 | C22×C3×C4 | — | 2 | 2 | no | — |
| 149 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 150 | C22×Dic3 | — | 2 | 2 | no | — |
| 151 | C22×Dic3 | — | 2 | 2 | no | — |
| 152 | C22×Dic3 | — | 2 | 1 | no | — |
| 153 | C22×Dic3 | #41 | 1 | 1 | yes | characteristic |
| 154 | C22×Dic3 | #41 | 1 | 1 | yes | characteristic |
| 155 | C3×Q16 | — | 2 | 2 | no | — |
| 156 | C3×SD16 | — | 2 | 4 | no | — |
| 157 | C3×D8 | — | 2 | 2 | no | — |
| 158 | C3×M16 | — | 2 | 2 | no | — |
| 159 | C3×M16 | — | 2 | 2 | no | — |
| 160 | C2×C3×C8 | — | 2 | 1 | no | — |
| 161 | C2×C3×C8 | — | 2 | 1 | no | — |
| 162 | C2×C3×C8 | — | 2 | 2 | no | — |
| 163 | C2×C3×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 164 | C2×C3×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 165 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×C3×C8 | #41 | 1 | 2 | yes | — |
| 168 | C2×C3×C8 | #41 | 1 | 2 | yes | — |
| 169 | C3×C42 | — | 2 | 1 | no | — |
| 170 | C3×C42 | — | 2 | 1 | no | — |
| 171 | #217 | — | 2 | 2 | no | — |
| 172 | #217 | — | 2 | 2 | no | — |
| 173 | #217 | — | 2 | 2 | no | — |
| 174 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 175 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 176 | C4⋊Dic3 | C22×C4 | 1 | 2 | yes | — |
| 177 | C4⋊Dic3 | C22×C4 | 1 | 2 | yes | — |
| 178 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 179 | C4×Dic3 | — | 2 | 2 | no | — |
| 180 | C4×Dic3 | — | 2 | 2 | no | — |
| 181 | C4×Dic3 | — | 2 | 2 | no | — |
| 182 | C4×Dic3 | — | 2 | 1 | no | — |
| 183 | C4×Dic3 | — | 2 | 1 | no | — |
| 184 | C4×Dic3 | C22×C4 | 1 | 2 | yes | — |
| 185 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 186 | #208 | — | 2 | 2 | no | — |
| 187 | #208 | — | 2 | 2 | no | — |
| 188 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 189 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 190 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 191 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 192 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 193 | C2×C3⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 194 | C2×C3⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 195 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 196 | #135 | — | 2 | 2 | no | — |
| 197 | #135 | — | 2 | 2 | no | — |
| 198 | C2×Q16 | C4×D3 | 1 | 1 | yes | characteristic |
| 199 | C2×SD16 | C4×D3 | 1 | 2 | yes | — |
| 200 | C2×D8 | C4×D3 | 1 | 1 | yes | characteristic |
| 201 | C2×M16 | — | 3 | 2 | no | — |
| 202 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 203 | C22×C8 | — | 3 | 1 | no | — |
| 204 | C22×C8 | — | 3 | 1 | no | — |
| 205 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 206 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 207 | C4×Q8 | — | 3 | 2 | no | — |
| 208 | C4×Q8 | — | 3 | 2 | no | — |
| 209 | C4×D4 | — | 3 | 2 | no | — |
| 210 | C4×D4 | — | 3 | 2 | no | — |
| 211 | C4×D4 | — | 6 | 2 | no | — |
| 212 | C4×D4 | — | 6 | 2 | no | — |
| 213 | #117 | — | 3 | 2 | no | — |
| 214 | #117 | — | 6 | 2 | no | — |
| 215 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 216 | C2×C42 | — | 3 | 1 | no | — |
| 217 | C2×C42 | — | 3 | 1 | no | — |
| 218 | C2×C42 | — | 6 | 2 | no | — |
| 219 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 220 | #108 | — | 2 | 2 | no | — |
| 221 | #108 | — | 6 | 2 | no | — |
| 222 | #108 | — | 12 | 2 | no | — |
| 223 | #107 | — | 3 | 1 | no | — |
| 224 | #107 | — | 3 | 1 | no | — |
| 225 | #106 | — | 3 | 2 | no | — |
| 226 | C4⋊C8 | — | 3 | 2 | no | — |
| 227 | C4⋊C8 | — | 3 | 2 | no | — |
| 228 | C4⋊C8 | — | 6 | 2 | no | — |
| 229 | C4⋊C8 | — | 6 | 2 | no | — |
| 230 | #104 | — | 4 | 2 | no | — |
| 231 | #104 | — | 12 | 2 | no | — |
| 232 | #103 | — | 3 | 2 | no | — |
| 233 | #103 | — | 3 | 2 | no | — |
| 234 | #102 | — | 3 | 2 | no | — |
| 235 | #102 | — | 3 | 2 | no | — |
| 236 | C22⋊C8 | — | 2 | 2 | no | — |
| 237 | C22⋊C8 | — | 2 | 2 | no | — |
| 238 | C22⋊C8 | — | 6 | 2 | no | — |
| 239 | C22⋊C8 | — | 6 | 2 | no | — |
| 240 | #97 | — | 3 | 2 | no | — |
| 241 | #97 | — | 3 | 2 | no | — |
| 242 | #97 | — | 6 | 2 | no | — |
| 243 | #97 | — | 6 | 2 | no | — |
| 244 | #97 | — | 6 | 2 | no | — |
| 245 | C4×C8 | — | 2 | 2 | no | — |
| 246 | C4×C8 | — | 6 | 2 | no | — |
| 247 | C4×C8 | — | 6 | 2 | no | — |
| 248 | #95 | — | 6 | 1 | no | — |
| 249 | C23×C3 | — | 2 | 2 | no | — |
| 250 | C23×C3 | C2×#41 | 1 | 1 | yes | characteristic |
| 251 | C3×Q8 | — | 2 | 2 | no | — |
| 252 | C3×Q8 | — | 2 | 2 | no | — |
| 253 | C3×D4 | — | 2 | 2 | no | — |
| 254 | C3×D4 | — | 2 | 2 | no | — |
| 255 | C3×D4 | — | 4 | 2 | no | — |
| 256 | C3×D4 | — | 4 | 2 | no | — |
| 257 | C2×C3×C4 | — | 2 | 2 | no | — |
| 258 | C2×C3×C4 | — | 2 | 2 | no | — |
| 259 | C2×C3×C4 | — | 4 | 1 | no | — |
| 260 | C2×C3×C4 | — | 4 | 1 | no | — |
| 261 | C2×C3×C4 | — | 4 | 2 | no | — |
| 262 | C2×C3×C4 | — | 4 | 2 | no | — |
| 263 | C2×C3×C4 | C23×C4 | 1 | 1 | yes | characteristic |
| 264 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 265 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 266 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 267 | C2×C3×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 268 | C2×C3×C4 | 2−1+4 | 1 | 1 | yes | characteristic |
| 269 | C2×Dic3 | — | 2 | 2 | no | — |
| 270 | C2×Dic3 | — | 2 | 2 | no | — |
| 271 | C2×Dic3 | — | 4 | 1 | no | — |
| 272 | C2×Dic3 | — | 4 | 1 | no | — |
| 273 | C2×Dic3 | — | 4 | 4 | no | — |
| 274 | C2×Dic3 | — | 4 | 1 | no | — |
| 275 | C2×Dic3 | — | 4 | 1 | no | — |
| 276 | C2×Dic3 | — | 4 | 1 | no | — |
| 277 | C2×Dic3 | — | 8 | 2 | no | — |
| 278 | C2×Dic3 | C4×D4 | 1 | 2 | yes | — |
| 279 | C2×Dic3 | C4×D4 | 1 | 2 | yes | — |
| 280 | C3×C8 | — | 2 | 1 | no | — |
| 281 | C3×C8 | — | 2 | 1 | no | — |
| 282 | C3×C8 | — | 4 | 2 | no | — |
| 283 | C3×C8 | #117 | 1 | 2 | yes | — |
| 284 | C3×C8 | #117 | 1 | 2 | yes | — |
| 285 | C3⋊C8 | — | 2 | 2 | no | — |
| 286 | C3⋊C8 | — | 2 | 2 | no | — |
| 287 | C3⋊C8 | — | 4 | 2 | no | — |
| 288 | #41 | — | 2 | 2 | no | — |
| 289 | #41 | — | 2 | 2 | no | — |
| 290 | #41 | — | 2 | 2 | no | — |
| 291 | #41 | — | 2 | 2 | no | — |
| 292 | C2×Q8 | C2×C4×D3 | 1 | 2 | yes | — |
| 293 | C2×D4 | — | 2 | 2 | no | — |
| 294 | C2×D4 | C2×C4×D3 | 1 | 2 | yes | — |
| 295 | C22×C4 | — | 2 | 1 | no | — |
| 296 | C22×C4 | — | 2 | 2 | no | — |
| 297 | C22×C4 | — | 3 | 1 | no | — |
| 298 | C22×C4 | — | 3 | 1 | no | — |
| 299 | C22×C4 | — | 6 | 2 | no | — |
| 300 | C22×C4 | — | 6 | 2 | no | — |
| 301 | C22×C4 | — | 6 | 1 | no | — |
| 302 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 303 | Q16 | — | 2 | 2 | no | — |
| 304 | SD16 | — | 2 | 4 | no | — |
| 305 | D8 | — | 2 | 2 | no | — |
| 306 | M16 | — | 2 | 2 | no | — |
| 307 | M16 | — | 2 | 2 | no | — |
| 308 | M16 | — | 6 | 2 | no | — |
| 309 | M16 | — | 6 | 2 | no | — |
| 310 | C2×C8 | — | 2 | 1 | no | — |
| 311 | C2×C8 | — | 2 | 1 | no | — |
| 312 | C2×C8 | — | 2 | 2 | no | — |
| 313 | C2×C8 | — | 3 | 2 | no | — |
| 314 | C2×C8 | — | 3 | 2 | no | — |
| 315 | C2×C8 | — | 6 | 1 | no | — |
| 316 | C2×C8 | — | 6 | 1 | no | — |
| 317 | C2×C8 | — | 6 | 1 | no | — |
| 318 | C2×C8 | — | 6 | 1 | no | — |
| 319 | C2×C8 | — | 6 | 2 | no | — |
| 320 | C2×C8 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 321 | C2×C8 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 322 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 323 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 324 | C2×C8 | #237 | 1 | 2 | yes | — |
| 325 | C2×C8 | #237 | 1 | 2 | yes | — |
| 326 | C4⋊C4 | — | 3 | 2 | no | — |
| 327 | C4⋊C4 | — | 3 | 2 | no | — |
| 328 | C4⋊C4 | — | 6 | 2 | no | — |
| 329 | C4⋊C4 | — | 6 | 2 | no | — |
| 330 | C4⋊C4 | — | 12 | 2 | no | — |
| 331 | C22⋊C4 | — | 6 | 2 | no | — |
| 332 | C22⋊C4 | — | 6 | 2 | no | — |
| 333 | C22⋊C4 | — | 6 | 2 | no | — |
| 334 | C42 | — | 2 | 1 | no | — |
| 335 | C42 | — | 2 | 1 | no | — |
| 336 | C42 | — | 3 | 2 | no | — |
| 337 | C42 | — | 3 | 2 | no | — |
| 338 | C42 | — | 6 | 2 | no | — |
| 339 | C42 | — | 6 | 2 | no | — |
| 340 | C42 | — | 6 | 2 | no | — |
| 341 | C42 | — | 6 | 1 | no | — |
| 342 | C42 | — | 6 | 1 | no | — |
| 343 | C22×C3 | — | 2 | 1 | no | — |
| 344 | C22×C3 | — | 2 | 1 | no | — |
| 345 | C22×C3 | — | 4 | 2 | no | — |
| 346 | C22×C3 | — | 4 | 2 | no | — |
| 347 | C22×C3 | — | 4 | 2 | no | — |
| 348 | C22×C3 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 349 | C22×C3 | #555 | 1 | 1 | yes | characteristic |
| 350 | C22×C3 | #556 | 1 | 1 | yes | characteristic |
| 351 | C3×C4 | — | 4 | 2 | no | — |
| 352 | C3×C4 | — | 4 | 2 | no | — |
| 353 | C3×C4 | C2×#117 | 1 | 1 | yes | characteristic |
| 354 | C3×C4 | #520 | 1 | 1 | yes | characteristic |
| 355 | C3×C4 | #547 | 1 | 1 | yes | characteristic |
| 356 | C3×C4 | #550 | 1 | 1 | yes | characteristic |
| 357 | Dic3 | — | 2 | 2 | no | — |
| 358 | Dic3 | — | 2 | 2 | no | — |
| 359 | Dic3 | — | 4 | 2 | no | — |
| 360 | Dic3 | — | 4 | 2 | no | — |
| 361 | Dic3 | — | 8 | 1 | no | — |
| 362 | C23 | — | 2 | 2 | no | — |
| 363 | C23 | D3×#41 | 1 | 1 | yes | characteristic |
| 364 | Q8 | — | 2 | 2 | no | — |
| 365 | Q8 | — | 2 | 2 | no | — |
| 366 | D4 | — | 2 | 2 | no | — |
| 367 | D4 | — | 2 | 2 | no | — |
| 368 | D4 | — | 4 | 2 | no | — |
| 369 | D4 | — | 4 | 2 | no | — |
| 370 | C2×C4 | — | 2 | 2 | no | — |
| 371 | C2×C4 | — | 2 | 2 | no | — |
| 372 | C2×C4 | — | 3 | 2 | no | — |
| 373 | C2×C4 | — | 3 | 2 | no | — |
| 374 | C2×C4 | — | 4 | 1 | no | — |
| 375 | C2×C4 | — | 4 | 1 | no | — |
| 376 | C2×C4 | — | 4 | 2 | no | — |
| 377 | C2×C4 | — | 4 | 2 | no | — |
| 378 | C2×C4 | — | 6 | 2 | no | — |
| 379 | C2×C4 | — | 6 | 2 | no | — |
| 380 | C2×C4 | — | 12 | 1 | no | — |
| 381 | C2×C4 | — | 12 | 1 | no | — |
| 382 | C2×C4 | — | 12 | 4 | no | — |
| 383 | C2×C4 | — | 12 | 1 | no | — |
| 384 | C2×C4 | — | 12 | 1 | no | — |
| 385 | C2×C4 | — | 12 | 1 | no | — |
| 386 | C2×C4 | — | 24 | 2 | no | — |
| 387 | C2×C4 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 388 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 389 | C2×C4 | C2×#237 | 1 | 1 | yes | characteristic |
| 390 | C2×C4 | C2×#237 | 1 | 1 | yes | characteristic |
| 391 | C2×C4 | #1004 | 1 | 1 | yes | characteristic |
| 392 | C2×C4 | #1010 | 1 | 1 | yes | characteristic |
| 393 | C8 | — | 2 | 1 | no | — |
| 394 | C8 | — | 2 | 1 | no | — |
| 395 | C8 | — | 4 | 2 | no | — |
| 396 | C8 | — | 6 | 2 | no | — |
| 397 | C8 | — | 6 | 2 | no | — |
| 398 | C8 | — | 12 | 2 | no | — |
| 399 | C8 | #877 | 1 | 2 | yes | — |
| 400 | C8 | #877 | 1 | 2 | yes | — |
| 401 | C2×C3 | — | 2 | 1 | no | — |
| 402 | C2×C3 | — | 2 | 1 | no | — |
| 403 | C2×C3 | — | 8 | 2 | no | — |
| 404 | C2×C3 | #2354 | 1 | 1 | yes | characteristic |
| 405 | C2×C3 | #2955 | 1 | 1 | yes | characteristic |
| 406 | C2×C3 | #2956 | 1 | 1 | yes | characteristic |
| 407 | C22 | — | 2 | 1 | no | — |
| 408 | C22 | — | 2 | 1 | no | — |
| 409 | C22 | — | 4 | 2 | no | — |
| 410 | C22 | — | 4 | 2 | no | — |
| 411 | C22 | — | 4 | 2 | no | — |
| 412 | C22 | C4×D3×D4 | 1 | 1 | yes | characteristic |
| 413 | C22 | #5616 | 1 | 1 | yes | characteristic |
| 414 | C22 | #5671 | 1 | 1 | yes | characteristic |
| 415 | C4 | — | 4 | 2 | no | — |
| 416 | C4 | — | 4 | 2 | no | — |
| 417 | C4 | — | 6 | 2 | no | — |
| 418 | C4 | — | 6 | 2 | no | — |
| 419 | C4 | — | 12 | 2 | no | — |
| 420 | C4 | — | 12 | 2 | no | — |
| 421 | C4 | — | 24 | 1 | no | — |
| 422 | C4 | C2×#877 | 1 | 1 | yes | characteristic |
| 423 | C4 | #5546 | 1 | 1 | yes | characteristic |
| 424 | C4 | #5611 | 1 | 1 | yes | characteristic |
| 425 | C4 | #5718 | 1 | 1 | yes | characteristic |
| 426 | C3 | #22804 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 427 | C2 | — | 2 | 1 | no | — |
| 428 | C2 | — | 2 | 1 | no | — |
| 429 | C2 | — | 8 | 2 | no | — |
| 430 | C2 | #76302 | 1 | 1 | yes | characteristic |
| 431 | C2 | #79888 | 1 | 1 | yes | characteristic |
| 432 | C2 | #79889 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta